Energy-momentum relation
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In special relativity, the energy-momentum relation is an relation between the energy, momentum and the mass of a body:
- <math> E^2 = m^2 c^4 + p^2 c^2, </math>
where c is the speed of light, E is total energy, m is invariant mass, and p is momentum.
For a body in its rest frame, the momentum is zero, so the equation simplifies to
- <math> E=mc^2 </math>
If the object is massless then the energy momentum relation reduces to
- <math> E=pc </math>
as is the case for a photon.
In natural units the energy-momentum relation can be expressed as
- <math> \omega^2 = m^2 + k^2 </math>
where ω is angular frequency, m is rest mass and k is wave number.
In Minkowski space, energy and momentum (the latter multiplied by a factor of c) can be seen as two components of a Minkowski four-vector. The norm of this vector is equal to the square of the rest mass of the body, which is a Lorentz invariant quantity and hence is independent of the frame of reference.
